On positive solutions of a class of nonlinear elliptic equations
type: Item
instance of: scholarly article
title: On positive solutions of a class of nonlinear elliptic equations
zbMATH Open document ID: 1165.35016
author: Mats Ehrnström
author: Octavian Mustafa
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2007-06-06T00:00:00Z
review text: The authors deal with the semilinear equation \[ \Delta_x u+ f(x,u)+ g(|x|)x\cdot\nabla u= 0\tag{1} \] in \(G_A= \{x\in\mathbb{R}^n:|x|> A\}\), \(n\geq 3\), and are interested in so-called asymptotically vanishing solutions. Under some mild hypotheses on \(f\) and \(g\), the existence of positive, asymptotically vanishing radial solutions for (1) is proved. To this end the authors use the sub-super solution technique as well as the strong maximum principle.
reviewed by: Messoud Efendiev
Mathematics Subject Classification ID: 35J60
Mathematics Subject Classification ID: 35B40
zbMATH DE Number: 5161914
zbMATH Keywords: positive solution
zbMATH Keywords: nonlinear elliptic equation
zbMATH Keywords: exterior domain
zbMATH Keywords: strong maximum principle
MaRDI profile type: Publication
full work available at URL: j.na.2006.07.002
OpenAlex ID: W2093666804
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DOI: 10.1016/J.NA.2006.07.002
description: scientific article; zbMATH DE number 5161914